## Abstract

In this paper we study several related problems of finding optimal interval and circular-arc covering. We present solutions to the maximum k-interval (k-circular-arc) coverage problems, in which we want to cover maximum weight by selecting k intervals (circular-arcs) out of a given set of intervals (circular-arcs), respectively, the weighted interval covering problem, in which we want to cover maximum weight by placing k intervals with a given length, and the k-centers problem. The general sets version of the discussed problems, namely the general measure k-centers problem and the maximum covering problem for sets are known to be NP-hard. However, for the one dimensional restrictions studied here, and even for circular-arc graphs, we present efficient, polynomial time, algorithms that solve these problems. Our results for the maximum k-interval and k-circular-arc covering problems hold for any right continuous positive measure on R.

Original language | English |
---|---|

Pages (from-to) | 281-295 |

Number of pages | 15 |

Journal | Annals of Operations Research |

Volume | 275 |

Issue number | 2 |

DOIs | |

State | Published - 15 Apr 2019 |

### Bibliographical note

Funding Information:Reuven Cohen thanks the BSF for support. Science and Technology of Israel.

Publisher Copyright:

© 2018, Springer Science+Business Media, LLC, part of Springer Nature.

## Keywords

- Covering
- Dynamic programming
- Optimization